An algorithm is presented for calculating stresses in graphite-based spherical fuel elements. The core of high-temperature gas-cooled reactors (VTGR) developed in the USSR contains spherical dispersion type fuel elements with graphite cladding and a core of matrix graphite. The fuel is UO/sub 2/. The fuel elements fall through special locks into the upper part of a spherical charge and move downward. The fast neutron fluence up to the end of the reactor operating life is 1.5 x 10/sup 21/cm/sup -2/. The variations of the temperature at the center of a fuel element, the temperature drop and the integrated flux of fast neutrons as functions of the displacement of a fuel element along the axis of the reactor are described. Stresses arise mainly from the nonuniform variation of the volume over the cross section of a fuel element, which is determined by the temperature distribution and the graphite shrinkage caused by neutron bombardment. The computational model for the analysis of thermal stresses in an elastic isotropic body is based on the linear relation between the components o /sub ik/ of the stress tensor and u /sub ik/ of the strain tansor.